A Note on the Extension of Continuous Convex Functions from Subspaces

Let Y be a subspace of a real normed space X. We say that the couple (X,Y) has the CE-property ("convex extension property") if each continuous convex function on Y admits a continuous convex extension defined on X.By using techniques of Johnson and Zippin, we prove the following results about the CE-property: if X is the c(0)(E)-sum or the l(p)(Gamma)-sum (1 < p < infinity) of separable normed spaces, then the couple (X,Y) has the CE-property, for each subspace Y of X. Another similar result concerns weak*-closed subspaces Y of X = l(1)(Gamma) = c(0)(Gamma*).